data driven heating energy load forecast modeling ...data driven heating energy load forecast...

Data Driven Heating Energy Load Forecast

Modeling Enhanced by Nonlinear Autoregressive

Exogenous Neural Networks

Jeong-A Ryu and Seongju Chang Korea Advanced Institute of Science and Technology/Civil and Environmental Engineering, Daejeon, South Korea

Email: [email protected], [email protected]

Abstract—As the building sector consumes considerable

portion of energy worldwide, effective management of

building energy is of great importance. In this regard,

forecasting building energy consumption is essential to use

and manage the energy efficiently. This paper describes

hourly heating energy load forecasting method with the load

dataset of National Renewable Energy Laboratory

(NREL)'s Research Support Facility (RSF) in the United

States using both typical Artificial Neural Network and

Nonlinear Autoregressive with Exogenous Inputs (NARX)

Neural Network. The accuracy of the model is evaluated by

MBE (Mean Bias Error) and CvRMSE (Coefficient of

Variation of the Root Mean Square Error). The NARX

neural network model showed a better performance than

typical ANN model and it is confirmed that the model

satisfies the acceptable error range proposed by ASHRAE

guideline 14. This research explored a way to build a better

performing neural network model for heating energy load

prediction based on accumulated dataset.

Index Terms—Building Energy, Heating Load Forecasting,

Artificial Neural Network (ANN), Nonlinear Autoregressive

with Exogenous Inputs (NARX) Neural Network

I. INTRODUCTION

Ref. [1] According to the report by the International

Energy Agency (IEA), buildings account for about one-

third of global primary energy consumption and about

one-third of total direct and indirect energy-related

greenhouse gas emissions. Therefore, efficient

management of building energy is required, and the

introduction of building energy management system is

gradually expanding in the building sector for efficient

use and management of energy. The core function of the

building energy management system is to enable in-depth

analysis of the various data generated in the building, and

the effective linkage of individual building components,

plant systems and the overall operation of the building

with the analysis results. Accurate load forecasting plays

an important role in building energy management systems.

It enables faster and more accurate energy analysis and an

effective energy utilization plan. It can affect contingency

planning, load shedding, management strategies and also

Manuscript received July 26, 2018; revised April 20, 2019.

commercialization strategies. Ref. [2,3] Accordingly,

various models for precise load prediction are actively

developed and applied. Those models can be mainly

divided into the statistical approaches such as ARIMA,

SARIMA, and ARMAX and the artificial intelligence

approaches such as ANN, SVM, and fuzzy logic. Ref. [4]

Due to the ease of use and adaptability to find the optimal

solutions in a rapid manner, the artificial intelligence

based approaches have gained popularity in recent years.

In this paper, we developed a neural network approach

using nonlinear autoregressive with exogenous input

model to forecast the heating energy load. Using the

power consumption data of the Research Support Facility

in the US National Renewable Energy Laboratory, the

artificial neural network model and the NARX neural

network model were developed and compared. The

accuracy of the model was evaluated by MBE and

CvRMSE tolerance proposed by ASHRAE guideline14.

The outline of the paper is structured as follows.

Section II describes the methodology of ANN and NARX

neural network. In Section III, it presents the model

development procedure and the results. Future work is

discussed in Section IV and the last section concludes the

paper.

II. METHODOLOGY

A Artificial Neural Network

Ref. [5, 6] ANN, which was introduced by McCulloh

and Pitts, is a biologically inspired technique that models

the nonlinear relationships. Neural networks have ability

to solve complex relationships, adaptive control, decision

making under uncertainty, and predictive patterns.

Typical ANN consists of input layer, hidden layer, and

output layer, each of which is made up of neurons

interconnected between different layers. Neurons are

connected by the weights and the activation function

converts the sum of the weighted inputs to the output.

Each weight is updated minimizing the error between the

generated output and the desired output mapping inputs

closer to the target with a learning algorithm. Fig.1 shows

the basic ANN architecture. The output of neuron can be

simply expressed as (1):

𝑦𝑖 = 𝑓(∑ 𝑥𝑗 ∙ 𝑤𝑖𝑗𝑛𝑗=1 ) (1)

246

International Journal of Structural and Civil Engineering Research Vol. 8, No. 3, August 2019

© 2019 Int. J. Struct. Civ. Eng. Res.doi: 10.18178/ijscer.8.3.246-252

where i is the index of the neuron in the layer, j is the

input index in the ANN, 𝑥𝑗 is the input vector, 𝑤𝑖𝑗is the

weight vector, and f is the activation function.

Figure 1. Ref. [7] Basic ANN Structure

B NARX(Nonlinear Autoregressive with Exogenous

Inputs) Neural Network

Ref. [8] NARX, which was proposed by Leontaritis

and billings, is a nonlinear model which estimates the

future values of the time series based on its outputs and

exogenous input. Ref. [9] It can represent wide variety of

nonlinear dynamic behaviors and have been used in

various applications. NARX model can be formulated as

(2):

y(𝑡 + 1) = 𝑓 (𝑦(𝑡), 𝑦(𝑡 − 1), … , 𝑦(𝑡 − 𝑛𝑦)

𝑥(𝑡), 𝑥(𝑡 − 1), … , 𝑥(𝑡 − 𝑛𝑥)) (2)

where x is input of the network at time t, y is output of

the network at time t, 𝑛𝑥 is input delay and 𝑛𝑦 is output

delay. The next value of the dependent output signal y is

estimated from previous values of the output signal and

independent input signal. Ref. [9] Depending on how the

function f is represented and parameterized, different

NARX model structures and algorithms are derived, and

neural network is used for this purpose in this study.

NARX network has two configurations which are

series-parallel architecture (open-loop form) as shown in

the left of Fig. 2 and parallel architecture (closed-loop

form) as shown in the right of Fig. 2. In the series-parallel

architecture, the true past values are used instead of

feeding back the estimated output values to predict the

future value of the time series. On the other hand, in the

parallel architecture, output values of the NARX network

are fed back to the input of the network to predict the

future value. During the training phase, the series-parallel

architecture is used and then after the training phase,

parallel architecture is used for multistep-ahead

prediction.

Figure 2. Ref. [7] NARX Neural Network Architecture

III. EXPERIMENTS AND RESULTS

A Dataset Description

In this paper, the power consumption of the National

Renewable Energy Laboratory (NREL)'s Research

Support Facility (RSF) in 2011 was used as dataset for

short-term load prediction. Ref. [10] The data provided

by the National Renewable Energy Laboratory is based

on the hourly power consumption measured by individual

instruments for the purposes of heating, cooling, lighting,

etc. from January 1 to December 31, 2011.

In this experiment, we used the heating energy demand

which is the largest proportion of the power consumption

and we used the part of the data of the winter period in

which heating equipment is frequently used. As training

data, the heating energy consumption, weather data (dry

bulb temperature, average global irradiation) on working

day (weekday) of 11/1 ~ 12/9 were used which consists

of a total of 696sets and we developed separate model for

one day-ahead forecasting model and one week(five days

for working day)-ahead forecasting model.

Using the input processing function “mapminmax” in

Matlab software, inputs and targets were normalized and

scaled to be in the range [-1,1]. Then, the trained network

provided outputs in the range [-1, 1] which were then

reverse-processed back into the same units as the original

targets. All simulations are performed in a Matlab

software environment.

B Artificial Neural Network Model Development

The composition of the ANN prediction model is

shown in Table I. The input variables consists of the dry

bulb temperature, average global irradiation and hour of

the day. Various configurations were tested by varying

the number of hidden neurons (1~20) and the number of

hidden layers (1~10) to find a network with optimal

performance. The tangent-sigmoid and pure linear

transfer functions were employed as the transfer functions

for the hidden and output neurons, respectively. The

feedforward network with Levenberg-Marquardt back-

propagation method was used for training the developed

neural network adapting weights between neurons

minimizing the error between the outputs of the network

and the targets. Cross-validation technique was

performed to control the training process.

247


© 2019 Int. J. Struct. Civ. Eng. Res.

TABLE I. COMPOSITION OF ANN MODEL

Model Components Contents

Structure

Input Layer

Number of neurons:3

(1) dry bulb temperature (2) average global irradiation

(3) hour of the day(0~23)

Hidden Layer Number of layers:1~10

Number of neurons:1~20

Output Layer Number of neurons:1

(1) heating consumption

Transfer

Function

Hidden Neurons Tangent Sigmoid

Output Neurons Pure Linear

Training

Method Algorithm Levenberg-Marquardt

To evaluate the performance of the models, following

metrics are used: CvRMSE(Coefficient of Variation of

the Root Mean Square Error), MBE(Mean Bias Error) are

formulated as (3) and (5), respectively.

Cv𝑅𝑀𝑆𝐸 =𝑅𝑀𝑆𝐸

𝑀𝑎𝑣𝑔× 100 (3)

𝑅𝑀𝑆𝐸 = √∑(𝑆−𝑀)2

𝑁 (4)

𝑀𝐵𝐸 =∑(𝑆−𝑀)

∑ 𝑀× 100 (5)

where S is estimated output, M is actual target data, N is

total number of data and 𝑀𝑎𝑣𝑔 is average of M.

To find a network with optimal performance, trial-

error procedure is conducted using a parametrical

optimization process. The number of hidden neurons and

hidden layers were sequentially optimized. After finding

the optimal value for the first component (hidden

neurons), the next component (hidden layers) was tested

with the fixed first component as the optimal value.

When finding the optimal value of the first component,

hidden layer was fixed to one layer. Separate models

were developed for one day-ahead forecasting model and

one week-ahead forecasting model, respectively. Table II

and Table III summarizes the parametrical values and the

performance of the network. The former is for one day-

ahead forecasting model and the latter is for one week-

ahead forecasting model.

TABLE II. ANN PARAMETRICAL OPTIMIZATION(1DAY)

Hidden Neurons

(Hidden layer:1)

Hidden Layers

(Hidden neurons:12,optimal result)

Hidden

neurons

Cv

RMSE

Hidden

neurons

Hidden

layers

Cv

RMSE MBE

1 50.04 12 1 28.49 -2.22

2 38.12 12 2 30.21 8.58

3 39.40 12 3 31.46 6.10

4 34.87 12 4 31.09 11.16

5 38.67 12 5 39.79 10.95

6 35.09 12 6 29.67 3.50

7 40.61 12 7 45.88 14.78

8 28.87 12 8 35.53 -0.14

9 35.38 12 9 40.27 6.17

10 34.98 12 10 31.63 -3.01

11 32.42

12 28.49

13 31.68

14 37.48

Hidden Neurons (Hidden layer:1)

Hidden Layers (Hidden neurons:12,optimal result)

Hidden

neurons

Cv

RMSE

Hidden

neurons

Hidden

layers

Cv

RMSE MBE

15 30.60

16 30.74

17 32.97

18 33.44

19 33.86

20 33.86

TABLE III. ANN PARAMETRICAL OPTIMIZATION(1WEEK)

Hidden Neurons (Hidden layer:1)

Hidden Layers (Hidden neurons:8,optimal result)

Hidden

neurons

Cv

RMSE

Hidden

neurons

Hidden

layers

Cv

RMSE MBE

1 54.28 8 1 29.70 -11.91

2 40.80 8 2 36.97 -11.81

3 40.27 8 3 35.01 -8.95

4 36.21 8 4 34.60 -9.01

5 43.31 8 5 37.84 -21.41

6 35.85 8 6 34.59 -7.15

7 39.55 8 7 34.60 -13.61

8 29.70 8 8 37.65 -7.45

9 35.70 8 9 36.81 -13.01

10 35.59 8 10 35.96 -7.81

11 30.86

12 31.13

13 34.05

14 36.38

15 30.66

16 33.93

17 34.84

18 35.30

19 35.99

20 33.44

As shown in Table II and Table III, optimal number of

hidden neurons and hidden layers can be found which

produced the least CvRMSE between the predicted and

the target value. The least value was obtained when the

ANN model employed twelve hidden neurons and one

hidden layer for one day-ahead forecasting model and

eight hidden neurons and one hidden layer for one week-

ahead forecasting model. Fig. 3 shows the example of the

configuration of the developed ANN model. The

CvRMSE between the predicted and the target value was

28.49 for the one day-ahead forecasting model and 29.70

for the one week-ahead forecasting model.

Figure 3. Matlab ANN Configuration

C NARX Neural Network Model Development

The composition of the NARX neural network

prediction model is shown in Table IV. Series-parallel

architecture (open-loop) is used for training phase which

means that the actual target values are feedback to the

network, and parallel architecture (closed-loop) is used

for testing phase which means that the estimated outputs

248



are fed back to the network. Various configurations were

tested by varying the number of hidden neurons (1~20)

and the number of delays (12~240) to find a network with

optimal performance. Delay parameter concerns the

number of hours the model is going to use to perform the

prediction.

TABLE IV. COMPOSITION OF NARX NEURAL NETWORK MODEL

Model Components Contents

Structure

Input Layer

Number of neurons:3

(1) dry bulb temperature (2) average global irradiation

(3) hour of the day(0~23)

Hidden Layer Number of layers:1

Number of neurons:1~20

Output Layer Number of neurons:1

(1) heating consumption

Delay 12~120 hours

Transfer Function

Hidden Neurons Tangent Sigmoid

Output Neurons Pure Linear

Training Method

Algorithm Levenberg-Marquardt

To find a network with optimal performance, the

number of hidden neurons and delays were sequentially

optimized with a parametrical optimization process. After

finding the optimal value for the first component (hidden

neurons), the next component (delay) was tested with the

fixed first component as the optimal value. When finding

the optimal value of the first component, delay parameter

was fixed to 60 hours. Separate models were developed

for one day-ahead forecasting model and one week-ahead

forecasting model, respectively. Table V and Table VI

summarizes the parametrical values and the performance

of the network. The former is for one day-ahead

forecasting model and the latter is for one week-ahead

forecasting model.

TABLE V. NARX NEURAL NETWORK PARAMETRICAL

OPTIMIZATION(1DAY)

Hidden Neuron

(Hidden layer:1,

Delay:60)

Delays (Hidden neurons:12,optimal result)

Hidden

neurons

Cv

RMSE

Hidden

neurons Delays

Cv

RMSE MBE

1 35.73 12 12 36.54 10.75

2 32.20 12 24 28.92 13.92

3 42.70 12 36 25.51 -13.97

4 39.65 12 48 40.23 9.69

5 40.74 12 60 18.87 -0.53

6 61.57 12 72 30.95 7.24

7 49.09 12 84 37.63 -3.93

8 50.38 12 96 26.85 2.06

9 61.14 12 108 64.96 -10.43

10 37.56 12 120 24.34 -4.18

11 34.34

12 18.87

13 28.38

14 28.55

15 30.25

16 31.30

17 34.26

18 33.79

19 29.19

20 40.07

TABLE VI. NARX NEURAL NETWORK PARAMETRICAL

OPTIMIZATION(1WEEK)

Hidden Neuron (Hidden layer:1,

Delay:60)

Delays

(Hidden neurons:12,optimal result)

Hidden neurons

Cv RMSE

Hidden neurons

Delays Cv

RMSE MBE

1 37.62 12 12 46.73 23.29

2 44.21 12 24 44.86 35.57

3 73.55 12 36 27.68 -3.85

4 60.46 12 48 41.74 15.68

5 43.87 12 60 37.52 14.73

6 65.68 12 72 37.30 16.20

7 60.22 12 84 74.57 40.93

8 57.76 12 96 49.09 29.30

9 113.46 12 108 66.43 -4.83

10 49.85 12 120 32.45 1.77

11 43.68

12 37.52

13 37.56

14 46.12

15 58.43

16 46.73

17 54.92

18 50.27

19 45.24

20 44.90

As shown in Table V and Table VI, the least CvRMSE

value was obtained when the NARX neural network

model employed twelve hidden neurons and 60 hours

delay for one day-ahead forecasting model and twelve

hidden neurons and 36 hours delay for one week-ahead

forecasting model. Fig. 4 and Fig. 5 show the example of

the configuration of the developed NARX neural network

model for training phase and testing phase. The CvRMSE

between the predicted and the target value was 18.87 for

the one day-ahead forecasting model and 27.68 for the

one week-ahead forecasting model.

Figure 4. Matlab NARX Neural Network Series-Parallel Configuration(Training)

Figure 5. Matlab NARX Neural Network Pararell Configuration(Testing)

D Results

The results of the load forecasting of this study using

the ANN and NARX neural network are shown in the

following Table VII and Fig. 6, Fig. 7, Fig. 8, Fig. 9. The

249



developed ANN model employed twelve hidden neurons

and one hidden layer for one day-ahead forecasting

model and eight hidden neurons and one hidden layer for

one week-ahead forecasting model. The developed

NARX neural network model employed twelve hidden

neurons and 60 hours delay for one day-ahead forecasting

model and twelve hidden neurons and 36 hours delay for

one week-ahead forecasting model. Table VII

summarizes CvRMSE and MBE of each model.

TABLE VII. RESULTS OF CALIBRATION TOLERANCE INDEX

Forecasting

Period

(Working Day)

Index Artificial Neural

Network NARX Neural

Network

1 day

(24 hours)

CvRMSE 28.49 18.87

MBE -2.22 -0.53

1 week

(120 hours)

CvRMSE 29.70 27.68

MBE -11.91 -3.85

Ref. [11] The accuracy of the model was evaluated by

MBE and CvRMSE proposed by ASHRAE(American

Society of Heating, Refrigerating and Air-Conditioning

Engineers) as shown in Table VIII. According to the

ASHRAE guideline14 (2002), the recommended values

of MBE and CvRMSE for hourly measurements are

within ±10% and less than 30%, respectively.

TABLE VIII. TOLERANCES BY ASHRAE GUIDELINE 14

Calibration Type Index Acceptable Value

Hourly MBE ±10%

CvRMSE 30%

For one day-ahead forecasting model, both ANN

model (CvRMSE: 28.49, MBE: -2.22) and NARX neural

network model (CvRMSE: 18.87, MBE: -0.53) satisfied

the error range specified in Table VIII proposed by

ASHRAE guideline14. Therefore, developed model can

be regarded as reliable models. When comparing both

models, the NARX neural network model showed a better

performance than ANN model. It is easy to see that the

actual and predicted data in Fig. 7 fit better than in Fig. 6.

Figure 6. ANN Forecasting Results(one day-ahead)

Figure 7. NARX Forecasting Results(one day-ahead)

For one week-ahead forecasting model, only CvRMSE

(29.70) of ANN model satisfied the error range specified

in Table VIII. However, both CvRMSE (27.68) and

MBE(-3.85) of the NARX neural network model satisfied

the error range proposed by ASHRAE guideline14.

Therefore, developed NARX neural network model can

be regarded as reliable models. When comparing both

models, the NARX neural network model showed a better

performance than ANN model also for one-week ahead

forecasting model.

Figure 8. ANN Forecasting Results(one week-ahead)

Figure 9. NARX Forecasting Results(one week-ahead)

250



IV. DISCUSSION

We have focused on developing a better performing neural network model for heating energy load prediction using both typical ANN and NARX neural network model. Trial-error procedure is conducted using a parametrical optimization process to determine the optimal number of hidden neurons, hidden layers and

delays. The optimized parameter values were different for each model by the forecast period(one day-ahead or one week-ahead) and the developed model for the shorter term prediction showed a better performance which means that one day-ahead forecasting model (CvRMSE: 28.49/18.87) is more accurate than one week-ahead

forecasting model (CvRMSE: 29.70/27.68). When comparing the two neural networks, as shown in Table VII, the NARX neural network model provide better prediction than typical ANN model as the NARX neural network model has the additional information contained in the previous values of target value which is fed back to

the input. To develop better load forecasting model, future works

can be considered as follows.

1. The evolutionary optimization techniques can be

considered to determine the optimal network architecture

as the trial-error procedure cannot cover all cases.

2. The impact of various training algorithms on

predictive models can be investigated to select the best

suited algorithm.

3. Additional input factors can be explored which have

great influence on the load consumption to enhance the

performance of the forecast model.

4. As the size of training data has a great influence on

the accuracy, optimal training data size for each

forecasting period need to be explored and the best

interval to update the model can be derived.

5. Ensemble models can be constructed with the

combination of various AI based models compensating

the weaknesses of each single model.

V. CONCLUSION

In this paper, we developed hourly heating energy load

forecasting model using both typical ANN and NARX

neural network. We used the heating energy consumption

of the Research Support Facility(RSF) in 2011 provided

by the National Renewable Energy Laboratory(NREL) in

the United States. For training data, total 696sets which

are the hourly data on working day(weekday) of 11/1 ~

12/9 is used. We developed separate model for one day-

ahead forecasting model and one week(five days for

working day)-ahead forecasting model, respectively. Dry

bulb temperature, average global irradiation, hour of the

day(0~23) were used as inputs and trial-error procedure is

conducted using a parametrical optimization process to

determine the optimal number of hidden neurons, hidden

layers and delays. For one day-ahead forecasting model,

CvRMSE and MBE of ANN model were 28.49, -2.22 and

those of NARX neural network model were 18.87, -0.53.

For one week-ahead forecasting model, CvRMSE and

MBE of ANN model were 29.70, -11.91 and those of

NARX neural network model were 27.68, -3.85. One

day-ahead model showed better prediction than one

week-ahead model and in both cases, the NARX neural

network models performed better and also satisfy the

acceptable error range proposed by ASHRAE guideline

14.

The enhanced heating energy load forecast model was

developed taking advantage of both neural network which

can implicitly detect complex nonlinear relationships and

NARX network which have additional information

contained in the previous target values. The proposed

energy consumption forecasting model can be used for

effective building energy management system aiming of

energy conservation and reduced environmental impact.

ACKNOWLEDGMENT

This research was supported by the KUSTAR-KAIST

Institute, KAIST, Korea.

REFERENCES

[1] International Energy Agency, Transition to Sustainable Buildings: Strategies and Opportunities to 2050, Paris, 2013.

[2] C. Deb, F. Zhang, J. Yang, S. E. Lee, K. W. Shah, “A review on

time series forecasting techniques for building energy consumption,” Renewable and Sustainable Energy Reviews, vol.

74, pp. 902-924, June 2017.

[3] M. A. M. Daut, et al., “Building electrical energy consumption forecasting analysis using conventional and artificial intelligence

methods: A review,” Renewable and Sustainable Energy Reviews,

vol. 70, pp. 1108–1118, April 2017.

doi.org/10.1016/j.rser.2016.12.015

[4] Z. Wang, R. S. Srinivasan, “A review of artificial intelligence

based building energy use prediction: Contrasting the capabilities of single and ensemble prediction models,” Renewable and

Sustainable Energy Reviews, vol. 75, pp. 796–808, Aug. 2017.

[5] W. S. McCulloch and W. Pitts, “A logical calculus of the ideas immanent in nervous activity,” The Bulletin of Mathematical

Biophysics, vol. 5, no. 4, pp. 115-133, Dec. 1943.

[6] M. Q. Raza, A. Khosravi, “A review on artificial intelligence based load demand forecasting techniques for smart grid and

buildings,” Renewable and Sustainable Energy Reviews, vol. 50,

pp. 1352–1372, Oct. 2015. [7] Z. Boussaada, O. Curea, A. Remaci, H. Camblong, N. Mrabet

Bellaaj, “A nonlinear autoregressive exogenous (NARX) neural

network model for the prediction of the daily direct solar radiation,” Energies, vol. 11, no.3, 620, Mar. 2018.

[8] I. Leontaritis and S. Billings, “Input–output parametric models for

non-linear systems—part I: deterministic non-linear systems,”

International Journal of Control, vol. 41, pp. 303-328, 1985.

[9] E. Pisoni, M. Farina, C. Carnevale, and L. Piroddi, “Forecasting

peak air pollution levels using NARX models,” Engineering Applications of Artificial Intelligence, vol. 22, pp. 593-602, June

2009.

[10] M. Sheppy, A. Beach, S. Pless, “Metering best practices applied in the national renewable energy laboratory’s research support

facility. A Primer to the 2011 Measured and Modeled Energy

Consumption Datasets,” US, Apr. 2013. [11] ASHRAE, ASHRAE Guideline 14-2002 Measurement of Energy

and Demand Savings, Atlanta, 2002.

Jeong-A Ryu received the bachelor’s degree in electrical engineering from Korea University,

Seoul, Korea in 2012. She is currently attending a master’s course in civil and environmental

engineering at Korean Advanced Institute of

Science and Technology (KAIST), Daejeon, Korea. Her research interests include building

energy management systems and IOT

applications in building systems.

251



Seongju

Chang

is an expert in the field of smart

& green building systems. He is currently an invited professor of the department of Civil &

Environmental Engineering at KAIST, Korea.

Prof. Seongju Chang got his bachelor’s and master’s degrees at Seoul National University in

Korea majoring in architecture and received Ph.D.

degree in Building Performance & Diagnostics at Carnegie Mellon University, Pittsburgh, USA in

1999. His current research interest includes various smart and

sustainable architectural/urban systems including smart building components, energy efficient and resource circulative sustainable

buildings and cities. He is also listed on the Marquis Who’s Who as one

of the potential contributors for resolving World’s problems.

252



data driven heating energy load forecast modeling ...data driven heating energy load forecast...

Documents